From Theory to Practice: Derivative-Free Optimization, Bilevel Problems, and Real-World Applications

Prof. Remigijus Paulavičius
Vilnius University, Lithuania

Abstract

This talk explores the journey from theory to practice in derivative-free optimization (DFO), primarily focusing on the impact of DIRECT-type algorithms and their application to practical problems. While focusing on this key aspect, the presentation also delves into several other pertinent areas of mathematical optimization, such as bilevel optimization, offering a broader perspective on the field’s advancements and challenges. The presentation begins with an overview of the DIRECT algorithm’s role in DFO, highlighting its strengths and limitations. The subsequent discussion delves into advancements in DIRECT-type algorithms and their integration into software tools, facilitating practical applications. The talk presents a comparative analysis of deterministic and stochastic DFO methods through benchmarking studies, evaluating their performance and suitability for various problem domains. Then, the author showcases his contributions to the bilevel optimization field, where he worked on a general bilevel algorithm and underscored the critical need for such algorithms and software tools in practical applications, including ML. Finally, the talk showcases successful collaborations between academia and industry, highlighting the practical implementation of DFO techniques in real-world scenarios with examples from GlobeTrott Travel and Girteka Logistics, demonstrating the impact of DFO in solving complex optimization problems in business settings.

Schedule

June 19th, 10:00-12:00 (Palazzo delle Scienze, Aula Magna Matematica)